Linear B-spline finite element method for the improved Boussinesq equation
In this paper, we develop and validate a numerical procedure for solving a class of initial boundary value problems for the improved Boussinesq equation. The finite element method with linear B-spline basis functions is used to discretize the nonlinear partial differential equation in space and deri...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Elsevier
2008
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| Online Access: | http://hdl.handle.net/20.500.11937/41900 |
| _version_ | 1848756271673507840 |
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| author | Lin, Qun Wu, Yong Hong Loxton, Ryan Lai, Shaoyong |
| author_facet | Lin, Qun Wu, Yong Hong Loxton, Ryan Lai, Shaoyong |
| author_sort | Lin, Qun |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we develop and validate a numerical procedure for solving a class of initial boundary value problems for the improved Boussinesq equation. The finite element method with linear B-spline basis functions is used to discretize the nonlinear partial differential equation in space and derive a second order system involving only ordinary derivatives. It is shown that the coefficient matrix for the second order term in this system is invertible. Consequently, for the first time, the initial boundary value problem can be reduced to an explicit initial value problem to which many accurate numerical methods are readily applicable. Various examples are presented to validate this technique and demonstrate its capacity to simulate wave splitting, wave interaction and blow-up behavior. |
| first_indexed | 2025-11-14T09:09:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-41900 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:09:33Z |
| publishDate | 2008 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-419002019-02-19T04:26:54Z Linear B-spline finite element method for the improved Boussinesq equation Lin, Qun Wu, Yong Hong Loxton, Ryan Lai, Shaoyong In this paper, we develop and validate a numerical procedure for solving a class of initial boundary value problems for the improved Boussinesq equation. The finite element method with linear B-spline basis functions is used to discretize the nonlinear partial differential equation in space and derive a second order system involving only ordinary derivatives. It is shown that the coefficient matrix for the second order term in this system is invertible. Consequently, for the first time, the initial boundary value problem can be reduced to an explicit initial value problem to which many accurate numerical methods are readily applicable. Various examples are presented to validate this technique and demonstrate its capacity to simulate wave splitting, wave interaction and blow-up behavior. 2008 Journal Article http://hdl.handle.net/20.500.11937/41900 10.1016/j.cam.2008.05.049 Elsevier fulltext |
| spellingShingle | Lin, Qun Wu, Yong Hong Loxton, Ryan Lai, Shaoyong Linear B-spline finite element method for the improved Boussinesq equation |
| title | Linear B-spline finite element method for the improved Boussinesq equation |
| title_full | Linear B-spline finite element method for the improved Boussinesq equation |
| title_fullStr | Linear B-spline finite element method for the improved Boussinesq equation |
| title_full_unstemmed | Linear B-spline finite element method for the improved Boussinesq equation |
| title_short | Linear B-spline finite element method for the improved Boussinesq equation |
| title_sort | linear b-spline finite element method for the improved boussinesq equation |
| url | http://hdl.handle.net/20.500.11937/41900 |